Determination of the IsVisible value takes all factors of layout into account. In contrast, Visibility, which is a settable property, only indicates the intention to programmatically make an element visible or invisible.
Changes to the value of this property will typically raise the IsVisibleChanged event. There is no matching Microsoft .NET "On*" class handling override method that would allow some derived class to override that behavior and handle the event, but a class handler could still be attached directly with RegisterClassHandler.
Elements where IsVisible is false do not participate in input events (or commands), do not influence either the measure or arrange passes of layout, are not focusable, are not in a tab sequence, and will not be reported in hit testing. In contrast, elements where IsEnabled is false will still participate in events and commands, and hit testing, but are also not focusable.
IsVisible is not intended to be used as a style trigger. Using IsVisible as a style trigger might have unpredictable results. IsVisible is intended for state checking by lower level input implementations.